A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis H0: µ = 12 against H1: µ < 12 using a random sample of n = 4 specimens. Calculate the P-value if the observed statistic is Xbar (average) = 11.25. Suppose that the distribution of the sample mean is approximately normal.

The p-value of the test is 0.0013.

Step-by-step explanation:

The test statistic is:

In which X is the sample mean, is the value tested at the null hypothesis, is the standard deviation and n is the size of the sample.

12 is tested at the null hypothesis:

This means that

Standard deviation of 0.5 kilograms.

This means that

Sample of n = 4 specimens. Observed statistic is Xbar (average) = 11.25.  

This means that

Value of the test statistic:

P-value:

Probability of finding a sample mean belo 11.25, which is the p-value of z = -3.

Looking at the z-table, z = -3 has a p-value of 0.0013, thus the this is the p-value of the test.

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step-by-step explanation: